已知f(x)=sin(x+π/3),若α∈(-π/6,π/6),且f(α)=3/5,试求cosα的值

Question

已知f(x)=sin(x+π/3),若α∈(- π/6,π/6),且f(α)=3/5,试求cosα的值

Answer 1

由条件知f(α)=sin(α+π/3)=3/5,
α∈(- π/6,π/6),
α+π/3∈(π/6,π/2),为第一象限角
所以cos(α+π/3)=4/5
cosα=cos(α+π/3-π/3)
=sin(α+π/3)sin(π/3)+cos(α+π/3)cos(π/3)
= 3/5 * √3 /2+4/5* 1/2
=(3√3 +4)/10